John M. Dealy

Wall slip of molten high density polyethylenes. II. Capillary rheometer studies

Above the critical stress for slip, the procedures normally used to analyze the results of capillary flow data give anomalous results. In particular, the Bagley plots are curved, even when a variation of viscosity with pressure is not anticipated, and the Mooney technique used to calculate the slip velocity gives results that indicate that the slip velocity depends on the L/D ratio. It is proposed that these phenomena arise from the dependence of the slip velocity on the wall normal stress, which implies a dependence on pressure. Based on this hypothesis, an approximate method is developed for interpreting the results of capillary flow experiments to determine the slip velocity as a function of both the wall shear stress and the pressure. The large available data set was used to incorporate into the model the effects of molecular weight parameters and temperature on the slip velocity. Finally, a detailed model for slip flow in a capillary was formulated that takes into account that the slip velocity and wall shear stress vary along the flow direction due to the pressure gradient. This model was used to evaluate the validity of the approximations used in the approximate data analysis technique for determining the slip velocity.

Wall slip of molten high density polyethylene. I, Sliding plate rheometer studies

Experiments were performed in a sliding plate rheometer with a high density polyethylene to determine the conditions for the onset of slip and the relationship between slip velocity and shear stress. It was found that melt slip occurs at a critical shear stress of approximately 0.09 MPa in both steady and transient shear tests. The effect of the presence of a layer of fluorocarbon at the interface on both the slip velocity and the critical shear stress for the onset of slip, was also studied. Exponential shear was used to study the effect of shear history on slip. Both steady state and dynamic models for the slip velocity are proposed that are consistent with the experimental observations. Results of oscillatory shear experiments suggest that melt slip is a physicochemical process in which the polymer–wall interface undergoes continuous change during successive cycles.

Role of slip and fracture in the oscillating flow of HDPE in a capillary

Certain polymers exhibit two distinct branches in their capillary flow curves (wall shear stress versus apparent wall shear rate). This gives rise to oscillatory flow in constant‐piston‐speed rheometers and to flow curve hysteresis in controlled‐pressure rheometers. These curious phenomena have attracted considerable interest over a period of many years, but their basic mechanisms are still the subject of debate. Building on previous work we have developed a model that predicts all the essential features of the curves of pressure and flow rate versus time in the oscillatory flow regime. Fluid compressibility and the second branch of the flow curve are necessary features of the model, but fluid elasticity is found not to be an essential element. While our macroscopic measurements do not prove it conclusively, our data lead us to believe that on the high‐flow‐rate branch of the flow curve there is slip along a cylindrical fracture surface near the wall. The jump to the high‐flow branch occurs when this fracture occurs, at an upper critical value of the shear stress, while the jump back to the low‐flow branch occurs when adhesion is established at the fracture surface at a lower critical shear stress.

Large-Amplitude Oscillatory Shear

Although linear viscoelastic properties can be measured in many ways, the small-amplitude oscillatory shear test is the most widely used method. Nonlinear viscoelastic properties can also be measured in many ways, but no predominant test method has emerged amongst experimentalists. Whereas there is a unifying theory that describes linear behavior, there is no unifying constitutive theory for nonlinear viscoelasticity. For this reason, each nonlinear test reveals a different aspect of a material’s behavior. Hence, experimentalists have designed various transient experiments to capture different features of nonlinear viscoelasticity.

Determination of the relaxation spectrum from oscillatory shear data

In order to use either a linear or nonlinear model of viscoelasticity to calculate the stress response of a material to various deformations, it is usually necessary to have available an explicit equation for the linear relaxation modulus G(t). The most popular procedure is to use the data from a small‐amplitude oscillatory shear experiment to determine the parameters of a generalized Maxwell model. However, this is an ill‐posed problem and is not at all a straightforward curve‐fitting operation. We compare three procedures for determining a set of relaxation times and discrete moduli that can then be used as empirical fitting parameters in fluid mechanics computations. These are linear regression, with and without regularization, and nonlinear regression. Nonlinear regression is found to give a good fit of the data with a minimum number of parameters.

Sliding plate rheometer studies of concentrated polystyrene solutions: Large amplitude oscillatory shear of a very high molecular weight polymer in diethyl phthalate

A very high molecular weight, narrow molecular weight distribution polystyrene, having a molecular weight of 8.42×106, was investigated using a sliding plate rheometer. The solvent was diethyl phthalate. The solution exhibited wall slip during steady shear, even at very low shear rates and exhibited a marked normal‐stress‐driven secondary flow at high shear rates. However, there was no evidence of slip during the oscillatory shear tests. Using fast Fourier transform analysis, the results of the oscillatory shear tests on this solution are presented in terms of response surfaces in a space based on a Pipkin diagram (strain‐rate amplitude versus frequency). These reveal the linear and nonlinear regimes and the approach to a purely elastic regime at high frequencies. Wagner’s constitutive equation predicts the major trends in the experimental data but does not provide quantitative predictions over the entire range of experimental parameters.

Strong Extensional and Shearing Flows of a Branched Polyethylene

Simultaneous fits of the Kaye‐BKZ and Wagner equations to shear and uniaxial extensional flow data are not the most critical tests of these equations, because their memory functions depend on two strain invariants, and this dependence can be varied independently for shear and for uniaxial extension to obtain a fit for each. In planar deformations, however, the memory function depends on only one invariant; this dependence can be measured in single‐step shear experiments, as is reported here for a branched polyethylene, IUPAC X, using a sliding plate rheometer. Predictions are then made for three different planar deformation histories: start‐up of steady simple shear and steady planar extension, and exponentially growing shear, all tests in which the memory function depends on only one invariant. The predictions in steady shear and exponential shear are in rough agreement with the data. The theory for planar extension, however, greatly underpredicts the experimental strain hardening of IUPAC X, which has been reported to be similar to the strain hardening usually seen in uniaxial extension for LDPE. Thus, the Kaye‐BKZ and Wagner single‐integral equations cannot simultaneously describe both strain softening in shear and extreme strain hardening in planar extension using a damping function obtained from one of these flows.

Wall slip and spurt flow of polybutadiene

Spurt occurs in the flow of entangled melts in a capillary rheometer in which the driving pressure is controlled. As the driving pressure increases, at a critical value there is a sudden increase in flow rate, often called spurt. This discontinuity is followed by another regime of smoothly increasing flow rate. A phenomenon that may contribute to this instability is a curve of wall shear stress versus slip velocity that has a maximum followed by a minimum, and there are models that predict such behavior. We used a sliding plate rheometer (SPR) to study wall slip for a highly entangled, linear polybutadiene at 1atm and at 46MPa. By varying the plate speed, we were able to explore the entire curve of shear stress versus slip velocity. This curve exhibited a maximum and a minimum in the stress, providing support for theories predicting this behavior and an explanation for the spurt effect in capillary rheometry. The spurt flow of the same polymer was also observed, and slip velocities were estimated and comp...

A high pressure sliding plate rheometer for polymer melts

A high-pressure sliding plate rheometer has been developed to investigate the effect of pressure on the rheological behavior of molten polymers and elastomers. The new rheometer operates at pressures up to 70 MPa and temperatures up to 225 °C. The sample is subjected to simple shear, and the resulting shear stress is measured locally using a shear stress transducer. This design eliminates the inhomogeneities in pressure and shear rate that occur in high pressure capillary and slit rheometers. Preliminary evaluation of the new instrument was carried out using a linear low density polyethylene. Viscosity curves were generated at pressures ranging from atmospheric pressure to 70 MPa, and the pressure coefficient of viscosity was determined. Experiments were also carried out in step strain and large amplitude oscillatory shear, demonstrating the new rheometer’s use to study the nonlinear viscoelastic behavior of molten polymers. Finally, this instrument was used to study strain-induced crystallization.

Validity of separable BKZ model for large amplitude oscillatory shear

Large amplitude oscillatory shear (LAOS) is a useful tool for the study of nonlinear viscoelasticity in polymeric liquids. To concisely describe the response of a material to such a test, it is desirable to make use of a constitutive equation. In this way, the response can be described in terms of the parameters of the rheological model. We have found a separable BKZ model, e.g., Wagner’s equation, to be useful in this regard for LDPE IUPAC X. The damping function determined in step shear experiments does not lead to accurate predictions of the LAOS response. For a given low frequency, however, it is possible to fit the parameters of a simple damping function equation to the LAOS response at one strain amplitude and to use these parameter values to reliably predict the response at other strain amplitudes. Thus, the Wagner equation provides a basis for the concise description of the response of LDPE IUPAC X to large amplitude oscillatory shear experiments at low frequencies. Conversely, it was found that the response of a HDPE melt to large amplitude oscillatory shear cannot be concisely described by the Wagner equation.